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"The formats differ in the way in which players are paired."
I suggest expanding this statement to:
"The formats differ in the way in which players are paired, and how the winner is determined."
I think the reason should be obvious. For example, once a player loses a game in the single knockout tournament format, he can never hope to win this tournment unlike the swiss format, while there is still a possibility for that player to win provided that nobody else wins all rounds (the players having same highest score may then be ordered via the messy tie breaker systems of SOS, SOSOS, etc.).
At the same time, the Hahn Pointing System will have a home to link from.
The Tournament Format and the determination of the winner are partly independent. Either the traditional win/loss count or the Hahn Point System? can be used for all the multi-round tournament formats but not for knockout tournaments.
Perhaps we should create a page for Tournament Scoring which details, or refers the reader to, both win/loss count scoring and Hahn scoring. Then we could describe tournaments as being round robin with Hahn scoring or round robin with win/loss scoring. There are also issues of seeding, eligibility, etc.
It seems to me that tournament format is really just the pairing method adopted by the tournament, whether its McMahon, double knockout, Swiss, Paramus or random.
Please look at the Tournaments page, 4. Holding a tournament heading for an initial move in this direction. The list of items may be incomplete.